Rectangular Number in Java

In this section, we will learn what is a rectangular number and also create Java programs to check if the given number is a rectangular number or not. The rectangular number program is frequently asked in Java coding interviews and academics.

Rectangular Number

A rectangular number is a positive integer that can be arranged in rectangular forms. It is also called as pronic or oblong numbers.

In simple words, rectangular number is a special type of number that makes the shape of a rectangle using an array, where the elements are arranged based on rows and columns.

Rectangular Number Example

The number 2 is a rectangular number because it forms a rectangle of 1 row and 2 columns.

The number 6 is a rectangular number because it forms a rectangle of 2 row and 3 columns,

Similarly, the number 8 is a rectangular number because it forms a rectangle of 2 row and 4 columns.

Note: The number 4 is the only even number that is not a rectangular number, because it forms square with array of 2 rows and 2 columns.

Not only even, but some odd numbers can also form a rectangular shape. For example, the number 15 can form rectangle of 3 rows and 5 columns, as shown below.

Some other rectangular numbers are:

0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420 …

We observe that we can calculate n^th rectangular number by using the following formula:

R_n = n(n + 1) or n² + n

Let's find the 4^th rectangular number.

Given number is 4.

R_n= n (n + 1)

R_n= n² + n

R₄= (4)²+ 4

R₄= 20

Hence, the 4^th rectangular number is 20.

Steps to Find Rectangular Number

Read or initialize a number N.
Calculate the square of the given number N and store it in a variable square.
Add the number (N) itself in the square that we get from the previous step.
We get the rectangular number.

Let's implement the above steps in a Java program.

Rectangular Number Java Program

Consider the following example to check whether given number is a rectangular number or not.

RectangularNumberTest.java

import java.util.Scanner;
public class RectangularNumberTest {
    // main method
    public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    // accept number from user
    System.out.println("Enter a number:");
    int num = in.nextInt();
    // finding the square root or number nearest to square root
    int sqrtNum = (int) Math.sqrt(num);
    // to check if the product of two consecutive numbers is 
    // equal to the given number
    if (num == (sqrtNum * (sqrtNum + 1))) {
        System.out.println( num + " is a rectangular number");
    }
    else {
        System.out.println( num + " is not a rectangular number");
    }
  }
}

Output:

Find n^th Rectangular Number

Consider following example where we print the n^th rectangular number, the value of n is provided by the user.

RectangularNumberExample.java

import java.util.Scanner;
public class RectangularNumberExample {
    //defining a function that returns n-th rectangular number
    public static int findRectangularNum (int n){
        return n * (n + 1);
    }
    //main method
    public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    //accept number from user
    System.out.println("Enter a number:");
    int num = in.nextInt();
    //calling the function to find rectangular number
    int res = findRectangularNum (num);
    //printing the number
    System.out.println("The " + num + "th rectangular number is: " + res);
  }
}

Output: